A note on vertex-reinforced random walks

A vertex-reinforced random walk on Z with exactly five points in its essential range exhibits the behavior described by Theorem 1.3 of Pemantle and Volkov (Ann. Probab. 27 (1999) 1368) almost surely.

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Bibliographic Details
Published in:Statistics & probability letters 2003-04, Vol.62 (3), p.275-280
Main Author: Dai, Jack Jie
Format: Article
Language:English
Subjects:
Convergent martingale
Exact sciences and technology
Mathematics
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Stochastic processes
Vertex-reinforced random walk
Vertex-reinforced random walk Convergent martingale
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Description
Summary:A vertex-reinforced random walk on Z with exactly five points in its essential range exhibits the behavior described by Theorem 1.3 of Pemantle and Volkov (Ann. Probab. 27 (1999) 1368) almost surely.
ISSN:0167-7152
1879-2103
DOI:10.1016/S0167-7152(03)00014-2